Question

rectangles have four right angles and opposite sides that are parallel.
a. is the figure shown a rectangle? explain.
b. if not, how could the points change so it would be a rectangle?
b. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
a. to make the figure a rectangle, change point c to (□, - 4).
b. to make the figure a rectangle, change point d to (□, 1).
c. to make the figure a rectangle, change point c to (6, - 4) and point d to (7, 1).
d. the figure shown is a rectangle.

Explanation:

Step1: Check if the figure is a rectangle

A rectangle has four right angles and opposite sides parallel. By observing the slopes of the sides (using the grid), we can see that the adjacent sides are not perpendicular (do not have slopes that are negative reciprocals). So, the figure is not a rectangle.

Step2: Determine the correct points for a rectangle

For a rectangle, if we assume the coordinates of \(A(-1,2)\), \(B(-1,-3)\). For the opposite side to be parallel and have right - angles, if we consider the horizontal and vertical relationships. If we want to form a rectangle, for point \(C\), if we follow the horizontal shift from \(B\) (same \(y\) - coordinate as \(C\) in the desired rectangle \(-4\)) and vertical shift from \(A\) (for the \(x\) - coordinate, similar to the horizontal shift from \(B\) to \(A\) in the \(x\) - direction). For point \(D\), if we follow the vertical shift from \(A\) ( \(y = 1\)) and horizontal shift from \(B\) ( \(x\) - coordinate calculation based on side - length consistency). After calculation (using the properties of rectangles: opposite sides are equal and parallel, adjacent sides are perpendicular), we find that changing point \(C\) to \((6,-4)\) and point \(D\) to \((7,1)\) will form a rectangle.

Answer:

a. No, the figure is not a rectangle because adjacent sides are not perpendicular (do not form right - angles as required for a rectangle).
b. C. To make the figure a rectangle, change point \(C\) to \((6, - 4)\) and point \(D\) to \((7,1)\)